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Outputs (6)

Passage-time moments and hybrid zones for the exclusion-voter model (2010)
Journal Article
MacPhee, I. M., Menshikov, M. V., Volkov, S., & Wade, A. R. (2010). Passage-time moments and hybrid zones for the exclusion-voter model. Bernoulli (Andover), 16(4), 1312-1342. https://doi.org/10.3150/09-bej243

We study the non-equilibrium dynamics of a one-dimensional interacting particle system that is a mixture of the voter model and the exclusion process. With the process started from a finite perturbation of the ground state Heaviside configuration con... Read More about Passage-time moments and hybrid zones for the exclusion-voter model.

A Markov chain model of a polling system with parameter regeneration (2007)
Journal Article
MacPhee, I. M., Menshikov, M., Petritis, D., & Popov, S. (2007). A Markov chain model of a polling system with parameter regeneration. Annals of Applied Probability, 17(5/6), 1447-1473. https://doi.org/10.1214/105051607000000212

We study a model of a polling system i.e. a collection of d queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is mapped to a mathem... Read More about A Markov chain model of a polling system with parameter regeneration.

Periodicity in the transient regime of exhaustive polling systems (2006)
Journal Article
MacPhee, I., Menshikov, M., Popov, S., & Volkov, S. (2006). Periodicity in the transient regime of exhaustive polling systems. Annals of Applied Probability, 16(4), 1816-1850. https://doi.org/10.1214/105051606000000376

We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the sequence of nodes... Read More about Periodicity in the transient regime of exhaustive polling systems.

Stability criteria for controlled queueing systems (2006)
Journal Article
MacPhee, I., & Müller, L. (2006). Stability criteria for controlled queueing systems. Queueing Systems, 52(3), 215-229. https://doi.org/10.1007/s11134-006-5555-x

We give an almost complete classification of ergodicity and transience conditions for a general multi-queue system with the following features: arrivals form Poisson streams and there are various routing schemes for allocating arrivals to queues; the... Read More about Stability criteria for controlled queueing systems.

Critical random walks on two-dimensional complexes with applications to polling systems (2003)
Journal Article
MacPhee, I., & Menshikov, M. (2003). Critical random walks on two-dimensional complexes with applications to polling systems. Annals of Applied Probability, 13(4), 1399-1422. https://doi.org/10.1214/aoap/1069786503

We consider a time-homogeneous random walk Xi = {xi (t)} on a two-dimensional complex. All of our results here are formulated in a constructive way. By this we mean that for any given random walk we can, with an expression using only the first and se... Read More about Critical random walks on two-dimensional complexes with applications to polling systems.